Mass spectrometers have been used for mass and intensity measurements of charged and uncharged elementary particles, electrons, atoms, and molecules. The components of a mass spectrometer are depicted in FIG. 1. The ion source 11 provides an original signal source to the mass spectrometer 12 which provides an instrument response. It is well known that the data collected by a detector and digitization system 13 can be represented in Cartesian coordinates, wherein mass, t, is along the abscissa and intensity, y(t), is along the ordinate (see, for example, FIGS. 2 and 3).
When a single impulse is detected by the mass spectrometer, the instrument can be characterized by an impulse response, h(t), as shown in FIG. 2 which depicts a model impulse response. Typically, however, more than one impulse is detected by the instrument. If the width of the impulse response is greater than the spacing between the impulses, then the output is a spectrum of an unresolved cluster of peaks, which is similar to that shown in FIG. 3, showing a mass spectrum, y(t), for C.sub.2 Cl.sub.4 which is Contrived Data of 4 AMU Wide Peaks. The Poisson noise associated with discrete particle detection as shown in FIG. 3 hides the desired exact information. The noise shown assumes 100 ions/sample at the top of the most abundant peak.
It is desirable to reconstruct mass/intensity information as depicted in FIG. 4, which shows the theoretically exact mass spectrum, s(t), for C.sub.2 Cl.sub.4.
It is known that the y(t) data, which is collected by the instrument, shown in FIG. 3, is the mathematical convolution of the two functions s(t) and h(t), (shown in FIGS. 4 and 2, respectively). The convolution of the two functions, which may be represented as s*h, smears the impulses at each mass by the response function. Again, the convolved output, y(t)=s(t)*h(t), is the data collected from the instrument.
The mathematics for convolution is well known, and the inverse of convolution may be easily expressed. It is desirable to obtain the inverse of the convolved output, that is, given h(t), deconvolve y(t), to obtain s(t), which represents the desired discrete information identifying the mass and intensity of the components of the sample.
An explanation of convolution is found in any text which includes a good discussion on Fourier transforms such as Numerical Recipes in C. The problem is that in real systems, there is noise associated with the observation of convolved system responses, and this noise is amplified by the mathematics of Fourier deconvolution to the point that the results are useless. There are also many iterative deconvolution methods which have seen limited success when the desired result is only several peaks.
A review which evaluates many of these methods has been published in Transactions on Instrumentation and Measurement, Vol. 40. No. 3. June 1991 pg. 558-562. titled A Quantitative Evaluation of Various Iterative Deconvolution Algorithms by Paul Benjamin Crilly. This paper shows results which are typical of the state of the art. Another recent publication demonstrates typical results for deconvolution of mass spectral data. International Journal of Mass Spectrometry and Ion Processes. 103 (1991) 67-79. is a paper titled The Regularized Inverse Convolution Approach to Resolving Overlapping Mass Spectral Peaks by V. V. Raznikov and M. 0. Raznikova. None of these methods makes the assumption that the peaks are located at regular intervals.